The same way as you would send a POST request, I believe:
$ perl -MLWP::UserAgent -e 'LWP::UserAgent->new->delete("http://localhost:9999/resource", Content => "data");'
On the debug side of a connection:
$ socat tcp-listen:9999 -
DELETE /resource HTTP/1.1
TE: deflate,gzip;q=0.3
Connection: TE, close
Host: localhost:9999
User-Agent: libwww-perl/6.04
Content-Length: 4
data